Dependent Structure Functions Research Articles

Silicon-tungsten calorimeter for the forward direction in the PHENIX experiment at RHIC

The PHENIX detector at RHIC has been designed to study hadronic and leptonic signatures of the Quark Gluon Plasma in heavy ion collisions and spin dependent structure functions in polarized proton collisions. The baseline detector measures muons in two muon spectrometers located forward and backward of mid-rapidity, and measures hadrons, electrons, and photons in two central spectrometer arms, each of which covers 90. in azimuth and 0.35 units of rapidity. Further progress requires extending rapidity coverage for hadronic and electromagnetic signatures by upgrading the functionality of the PHENIX muon spectrometers to include photon and jet measurement capabilities. Tungsten calorimeters with silicon pixel readout and fine transverse and longitudinal segmentation are proposed to attain this goal. The use of such a design provides the highest density and finest granularity possible in a calorimeter.

Silicon-tungsten calorimeter for the forward direction in the PHENIX experiment at RHIC

The PHENIX detector at RHIC has been designed to study hadronic and leptonic signatures of the Quark Gluon Plasma in heavy ion collisions and spin dependent structure functions in polarized proton collisions. The baseline detector measures muons in two muon spectrometers located forward and backward of mid-rapidity, and measures hadrons, electrons, and photons in two central spectrometer arms, each of which covers 90/spl deg/ in azimuth and 0.35 units of rapidity. Further progress requires extending rapidity coverage for hadronic and electromagnetic signatures by upgrading the functionality of the PHENIX muon spectrometers to include photon and jet measurement capabilities. Tungsten calorimeters with silicon pixel readout and fine transverse and longitudinal segmentation are proposed to attain this goal. The use of such a design provides the highest density and finest granularity possible in a calorimeter.

Higher twist analysis of the nucleong 1 structure function

Different methods to extract the polarized parton densities from the world polarized DIS data are considered. The higher twist correctionsh N (x)/Q 2 to the spin dependent proton and neutrong 1 structure functions are taken into account and found to be nonnegligible and important in the QCD analysis of the present experimental data. Their role in determining the polarized parton densities in the framework of the different approaches is discussed.

Inertial range scaling law

A model for inertial range intermittency and anomalous scaling of velocity structure functions is proposed. The Navier–Stokes equation is used to derive a basic Reynolds number dependent law for the instantaneous velocity difference between two points. This gives incomplete information about the dependence on scale and requires a statistical hypothesis in order to compute structure functions and other quantities. The specific assumptions made here relate the singular scaling exponent to the velocity amplitude. Anomalous exponents and Reynolds number dependent structure functions and velocity difference probability density functions are calculated which agree with the experiments.

Polarized quark distributions extracted from inclusive and semi-inclusive deeply inelastic scattering at HERMES

The helicity structure of the nucleon can be revealed by the determination of the spin dependent structure function g1(x,Q2). This has been done by the HERMES experiment with high precision by measuring double spin asymmetries in inclusive deep inelastic scattering of longitudinally polarized positrons on longitudinally polarized protons or deuterons. Furthermore, semi-inclusive asymmetries of hadrons, pions and kaons were extracted and used to perform a five component separation of the helicity distributions of u, $\bar u$ , d, $\bar d$ and s quarks in a LO QCD analysis. In general, the results agree well with phenomenological fits to inclusive data. While these fits predict a negative strange quark polarization, the HERMES result suggests a zero or slightly positive value. A possible breaking of the flavor symmetry of the polarized light sea $\Delta \bar u-\Delta \bar d$ was also investigated and found to be consistent with zero within the experimental precision.

Polarized structure functions in the valence quark and resonance regions and the GDH sum

I present in this paper the neutron spin physics program in Hall A at Jefferson Laboratory using a polarized 3He target. The program encompasses several completed experiments, in which, valuable spin observables (spin dependent structure functions) were measured in order to learn about how the nucleon spin arises from the behavior of the constituents. These experiments also offer a ground for testing our understanding of the strong regime of quantum chromodynamics (QCD) the theory of strong interactions through the determination of moments of these structure functions.

QCD at photon colliders

The novel possibilities of probing the photon structure and high energy limit of quantum chromodynamics (QCD) at photon colliders are summarised. We discuss the photon structure function F 2 γ( x, Q 2), the gluon distribution in the photon and the spin dependent structure function g 1 γ( x, Q 2) of the photon and emphasise advantages of the photon colliders for measuring these quantities. The possibility of probing the QCD pomeron and odderon in γγ and eγ collisions is also described.

Spin-dependent structure functions of real and virtual photons

The implications of the positivity constraint, $|g_1^{\gamma(P^2)}(x,Q^2)| \leq F_1^{\gamma(P^2)}(x,Q^2)$, on the presently unknown spin--dependent structure function $g_1^{\gamma(P^2)}(x,Q^2)$ of real and virtual photons are studied at scales $Q^2\gg P^2$ where longitudinally polarized photons dominate physically relevant cross sections. In particular it is shown how to implement the physical constraints of positivity and continuity at $P^2=0$ in NLO calculations which afford a nontrivial choice of suitable (DIS) factorization schemes related to $g_1^{\gamma}$ and $F_1^{\gamma}$ and appropriate boundary conditions for the polarized parton distributions of real and virtual photons. The predictions of two extreme `maximal' and `minimal' saturation scenarios are presented and compared with results obtained within the framework of a simple quark `box' calculation expected to yield reasonable estimates in the not too small regions of $x$ and $P^2$.

Impact parameter dependence of parton densities at low x

We consider impact parameter dependence of the polarized and unpolarized parton densities. Unitarity does not allow factorization of these structure functions over the Bjorken x and the impact parameter b variables. On the basis of the particular geometrical model approach, we conclude that spin of constituent quark may have a significant orbital angular momentum component which can manifest itself through the peripherality of the spin dependent structure functions.

Small-xbehavior of the nonsinglet polarized structure functiong2in the double logarithmic approximation

The nonsinglet spin dependent structure function $g_2(x,Q^2)$ is studied at small x within the double logarithmic approximation of perturbative QCD. Both positive and negative signature contributions are considered, and we find a power-like growth in $1/x$. We discuss how our result fits into the Wandzura-Wilczek relation.

QCD predictions for the spin dependent photonic structure functiong1γ(x,Q2)in the lowxregion of future linear colliders

The spin dependent structure function ${g}_{1}^{\ensuremath{\gamma}}{(x,Q}^{2})$ of the polarized photon is analyzed within the formalism based upon the unintegrated spin dependent parton distributions incorporating the LO Altarelli-Parisi evolution and the double ${\mathrm{ln}}^{2}(1/x)$ resummation at low values of Bjorken parameter x. We analyze the effects of the double ${\mathrm{ln}}^{2}(1/x)$ resummation on the behavior of ${g}_{1}^{\ensuremath{\gamma}}{(x,Q}^{2})$ in the low x region which may be accessible in future linear ${e}^{+}{e}^{\ensuremath{-}}$ and $e\ensuremath{\gamma}$ colliders. The sensitivity of the predictions on the possible nonperturbative gluon content of the polarized photons is analyzed. Predictions for spin dependent gluon distribution $\ensuremath{\Delta}{g}^{\ensuremath{\gamma}}{(x,Q}^{2})$ are also given.

Impact parameter dependence of low-xstructure functions

We consider impact parameter dependence of the polarized and unpolarized structure functions. Unitarity does not allow factorization of the structure functions over the Bjorken x and the impact parameter b variables. On the basis of the particular geometrical model approach we conclude that spin of constituent quark may have a significant orbital angular momentum component which can manifest itself through the peripherality of the spin dependent structure functions.

Spin dependent structure functiong1at lowxand lowQ2

A theoretical description of the spin dependent structure function ${g}_{1}{(x,Q}^{2})$ in the region of low values of x and ${Q}^{2}$ is presented. It contains the vector meson dominance contribution and the QCD improved parton model suitably extended to the low ${Q}^{2}$ domain. Theoretical predictions are compared with the recent experimental data in the low x, low ${Q}^{2}$ region.

Nucleon mass corrections to spin dependent structure functions and relations between their twist-3 contributions

The nucleon mass corrections are calculated to all polarized structure functions for neutral and charged current deep inelastic scattering in lowest order in the coupling constant. The impact of the target mass corrections on the general relations between the twist-2 and twist-3 parts of the structure functions is studied and three new relations between the twist-3 contributions are derived. The size of nucleon mass corrections for the g 1 and g 2 structure functions are estimated.

Polarized parton distribution in the relativistic quark exchange framework

The Spin dependent gluon and sea quark distributions of the proton and the neutron are extracted in the leading order (LO) and the next-to-leading order (NLO) QCD. The relativistic quark exchange model is used to calculate the related valence quark spin dependent structure function. The inverse Mellin transform technique is performed to evaluate the polarized x-dependent distributions of the gluon and the sea quark from the various moments of the valence quarks. It is shown that the calculated spin structure functions (SSF) of the proton and the neutron are in good agreement with the available data, such as E143, SMC, E142, E154 and Hermes experiments. A comparison is also made with the other theoretical models. Finally it is shown that the above calculated parton distributions improve the SSF of the proton and the neutron.

Chiral symmetry and the nucleon spin structure functions

We carry out a systematic investigation of twist-two spin dependent structure functions of the nucleon within the framework of the chiral quark soliton model (CQSM) by paying special attention to the role of chiral symmetry of QCD. The importance of chiral symmetry is illustrated through the good reproduction of the recent SLAC data for the neutron spin structure function ${g}_{1}^{n}{(x,Q}^{2}).$ We also observe a substantial difference between the predictions of the longitudinally polarized distribution functions and those of the transversity distribution functions. That the chiral symmetry may be responsible for this difference is seen in the isospin dependence of the corresponding first moments, i.e., the axial and tensor charges. The CQSM predicts ${g}_{A}^{(0)}{/g}_{A}^{(3)}\ensuremath{\simeq}0.25$ for the ratio of the isoscalar to isovector axial charges, while ${g}_{T}^{(0)}{/g}_{T}^{(3)}\ensuremath{\simeq}0.46$ for the ratio of the isoscalar to isovector tensor charges, which should be compared with the prediction ${g}_{A}^{(0)}{/g}_{A}^{(3)}{=g}_{T}^{(0)}{/g}_{T}^{(3)}=3/5$ of the constituent quark model or of the naive MIT bag model without proper account of chiral symmetry. Another prominent prediction of the CQSM is the opposite polarization of the $\ifmmode \bar{u}\else \={u}\fi{}$ and $\overline{d}$ antiquarks, thereby indicating the SU(2) asymmetric sea quark (spin) polarization in the nucleon.

Spin dependent structure function g1 at small x and small Q2

The QCD improved parton model description of the spin dependent structure function g1(x,Q2) based on the unintegrated spin dependent parton distributions is extended to the low Q2 region. Theoretical predictions are compared with the recent SMC data in the low x, low Q2 region.

FLAVOR-ASYMMETRIC SEA QUARK DISTRIBUTION IN A CHIRAL POTENTIAL MODEL

Flavor asymmetry of the sea quark distribution which expresses itself in the observed value of the Gottfried sum leads one to consider pion emission as directly contributing to the scale dependence of structure functions. As an example, we study the evolution of structure functions in a chiral potential model which incorporates the pion as the chiral-symmetry-restoring field and which was originally invented to explain the static properties of baryons. Evolution equations for the quark and pion densities are derived in the lowest order at subasymptotic Q2. The kernels of evolution for the effective quark densities turn out to be flavor-dependent and are endowed with properties quite distinct from those possessed by leading log QCD splitting functions. In particular, the commonly used probabilistic treatment of the evolution, which is legitimate in the kinematic region of the perturbative QCD evolution, is seen not to be valid in the domain of applicability of the chiral potential model. The model is shown to lead to nontrivial evolution of the nonsinglet moments in a manner consistent with the observed departure from the Gottfried sum rule in a low Q2 region. For higher Q2, the evolution of the Gottfried sum receives also an additive contribution not envisaged in the earlier works on the phenomenon.

Unified description of the non-singlet spin dependent structure function g1 incorporating Altarelli-Parisi evolution and the double logarithmic ln2(1/x) effects at low x

A unified equation for the non-singlet spin dependent structure function $g_1^{ns}(x,Q^2)$ which incorporates the complete leading order Altarelli-Parisi evolution at finite $x$ and double logarithmic $ ln^2(1/x)$ effects at $x \to 0$ is formulated. The solution of this equation reasonably agrees with the recent data obtained by the Spin Muon Collaboration.

On the $Q^2$ dependence of nuclear structure functions

The recent high statistics NMC data on the Tin to Carbon structure function ratio seems to indicate, for the first time, a significant Q 2 dependence, especially at small values of Bjorken x, x < 0.05, and Q 2 > 1 GeV2. A purely log(Q 2)-type dependence of the structure functions, which is consistent with the free nucleon data, yields a fairly flat ratio with little or no Q 2 dependence. In view of this seeming contradiction, we re-examine the applicability of such a model to nuclear structure functions in such a kinematical regime. We find that the model is consistent with all data, within experimental errors, without any need for introducing additional Q 2 dependences or higher twist contributions. The model correctly reproduces the Q 2 dependence of the Carbon structure function as well. We also critically examine the Q 2 dependence of the corresponding spin dependent structure functions.